binary search
DESCRIPTION
Binary Search. Binary search. Given value and sorted array a[] , find index i such that a[i] = value , or report that no such index exists. Invariant. Algorithm maintains a[lo] value a[hi]. Ex. Binary search for 33. 6. 13. 14. 25. 33. 43. 51. 53. 64. 72. 84. 93. - PowerPoint PPT PresentationTRANSCRIPT
821 3 4 65 7 109 11 12 14130
641413 25 33 5143 53 8472 93 95 97966
Binary Search
lo
Binary search. Given value and sorted array a[], find index isuch that a[i] = value, or report that no such index exists.
Invariant. Algorithm maintains a[lo] value a[hi].
Ex. Binary search for 33.
hi
Binary Search
Binary search. Given value and sorted array a[], find index isuch that a[i] = value, or report that no such index exists.
Invariant. Algorithm maintains a[lo] value a[hi].
Ex. Binary search for 33.
821 3 4 65 7 109 11 12 14130
641413 25 33 5143 53 8472 93 95 97966
lo himid
Binary Search
Binary search. Given value and sorted array a[], find index isuch that a[i] = value, or report that no such index exists.
Invariant. Algorithm maintains a[lo] value a[hi].
Ex. Binary search for 33.
821 3 4 65 7 109 11 12 14130
641413 25 33 5143 53 8472 93 95 97966
lo hi
Binary Search
Binary search. Given value and sorted array a[], find index isuch that a[i] = value, or report that no such index exists.
Invariant. Algorithm maintains a[lo] value a[hi].
Ex. Binary search for 33.
821 3 4 65 7 109 11 12 14130
641413 25 33 5143 53 8472 93 95 97966
lo mid hi
Binary Search
Binary search. Given value and sorted array a[], find index isuch that a[i] = value, or report that no such index exists.
Invariant. Algorithm maintains a[lo] value a[hi].
Ex. Binary search for 33.
821 3 4 65 7 109 11 12 14130
641413 25 33 5143 53 8472 93 95 97966
lo hi
Binary Search
Binary search. Given value and sorted array a[], find index isuch that a[i] = value, or report that no such index exists.
Invariant. Algorithm maintains a[lo] value a[hi].
Ex. Binary search for 33.
821 3 4 65 7 109 11 12 14130
641413 25 33 5143 53 8472 93 95 97966
lo himid
Binary Search
Binary search. Given value and sorted array a[], find index isuch that a[i] = value, or report that no such index exists.
Invariant. Algorithm maintains a[lo] value a[hi].
Ex. Binary search for 33.
821 3 4 65 7 109 11 12 14130
641413 25 33 5143 53 8472 93 95 97966
lohi
Binary Search
Binary search. Given value and sorted array a[], find index isuch that a[i] = value, or report that no such index exists.
Invariant. Algorithm maintains a[lo] value a[hi].
Ex. Binary search for 33.
821 3 4 65 7 109 11 12 14130
641413 25 33 5143 53 8472 93 95 97966
lohimid
Binary Search
Binary search. Given value and sorted array a[], find index isuch that a[i] = value, or report that no such index exists.
Invariant. Algorithm maintains a[lo] value a[hi].
Ex. Binary search for 33.
821 3 4 65 7 109 11 12 14130
641413 25 33 5143 53 8472 93 95 97966
lohimid